Question

A coin is tossed 150 times and the outcomes are recorded. The frequency distribution of the outcomes H (i.e. head) and T (i.e. tail) is given below:

Outcome	Head	Tail
Frequency	85	65

Find the value of P (H) i.e. probability of getting a head in a single trial.
A. P (H) =0.75 (approx)
B. P (H) =0.9 (approx)
C. P (H) =0.15 (approx)
D. None of these

Answer 1

Hint : Probability of an event is the ratio of Number of favorable outcomes and total number of outcomes. So note down the favorable outcomes of getting a head when a coin is tossed and total number of outcomes when the coin is tossed

** Complete step-by-step answer** :
We are given that a coin is tossed 150 times and the outcome is head 85 times and tail 65 times.
We have to find the value of P(H) i.e. probability of getting a head in a single trail.
Here when the coin is tossed 150 times, frequency of getting a head is 85 and the frequency of getting a tail is 65. So assume the frequency of getting head as the number of favorable outcomes of getting a head and total number of outcomes as 150.
Probability of an event is the ratio of Number of occurred favorable outcomes to the total number of possible outcomes. Here the event is getting a head when a coin is tossed.
$\Rightarrow P\left( H \right) = \dfrac{{No.of.favorable}}{{Total}} \\\ \Rightarrow P\left( H \right) = \dfrac{{85}}{{150}} \\\ \therefore P\left( H \right) = 0.5666 \approx 0.567 \\\$
But the value of probability we got is not matching with any of the given options.

So, the correct answer is “Option D”.

Note : Favorable outcomes define the possibility of happening of a particular event. In the above question, we have taken the frequency of getting heads as the favorable outcomes and the total number of times the coin tossed as total possible outcomes. The probability of an event is always less than or equal to 1. So be careful with the values of probabilities.